Non-transitive maps in phase synchronization

Murilo Da Silva Baptista; T. Pereira; J. C. Sartorelli; I. L. Caldas; Jurgen Kurths

doi:10.1016/j.physd.2005.10.003

Non-transitive maps in phase synchronization

Murilo Da Silva Baptista, T. Pereira, J. C. Sartorelli, I. L. Caldas, Jurgen Kurths

Physics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	216-232
Number of pages	17
Journal	Physica. D, Nonlinear Phenomena
Volume	212
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physd.2005.10.003
Publication status	Published - 15 Dec 2005

Keywords

chaotic phase synchronization
ergodic theory
temporal mappings
kicked logistic map
chaotic oscillators

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10.1016/j.physd.2005.10.003

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title = "Non-transitive maps in phase synchronization",

abstract = "Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved.",

keywords = "chaotic phase synchronization, ergodic theory, temporal mappings, kicked logistic map, chaotic oscillators",

author = "Baptista, {Murilo Da Silva} and T. Pereira and Sartorelli, {J. C.} and Caldas, {I. L.} and Jurgen Kurths",

year = "2005",

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doi = "10.1016/j.physd.2005.10.003",

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TY - JOUR

T1 - Non-transitive maps in phase synchronization

AU - Baptista, Murilo Da Silva

AU - Pereira, T.

AU - Sartorelli, J. C.

AU - Caldas, I. L.

AU - Kurths, Jurgen

PY - 2005/12/15

Y1 - 2005/12/15

N2 - Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved.

AB - Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved.

KW - chaotic phase synchronization

KW - ergodic theory

KW - temporal mappings

KW - kicked logistic map

KW - chaotic oscillators

U2 - 10.1016/j.physd.2005.10.003

DO - 10.1016/j.physd.2005.10.003

M3 - Article

SN - 0167-2789

VL - 212

SP - 216

EP - 232

JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

IS - 3-4

ER -

Non-transitive maps in phase synchronization

Abstract

Keywords

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